Chapter 4: Q 4.94 (page 450)

Evaluate the determinant $[\begin{matrix} 3 & - 2 & - 2 \\ 2 & - 1 & 4 \\ - 1 & 0 & - 3 \end{matrix}]$ , by expanding by minors along the first row.

Short Answer

Expert verified

The value of the determinant is 7

Step by step solution

Step 1. Given information

The given determinant is $[\begin{matrix} 3 & - 2 & - 2 \\ 2 & - 1 & 4 \\ - 1 & 0 & - 3 \end{matrix}]$

Step 2. Calculation

Expand by minors along the first row

$3 [\begin{matrix} - 1 & 4 \\ 0 & - 3 \end{matrix}] - (- 2) [\begin{matrix} 2 & 4 \\ - 1 & - 3 \end{matrix}] - 2 [\begin{matrix} 2 & - 1 \\ - 1 & 0 \end{matrix}] = 3 (3 - (4 \times 0)) + 2 ((2 \times - 3) - (- 1 \times 4)) - 2 (2 \times 0 - (- 1 \times - 1)) = 3 [3] + [2 (- 6 + 4)] - [2 (0 - 1)] = 3 [3] - [4] + [2] = 9 - 4 + 2 = 7$

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Evaluate the determinant $[\begin{matrix} 3 & - 2 & - 2 \\ 2 & - 1 & 4 \\ - 1 & 0 & - 3 \end{matrix}]$ , by expanding by minors along the first row.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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Evaluate the determinant $[\begin{matrix} 3 & - 2 & - 2 \\ 2 & - 1 & 4 \\ - 1 & 0 & - 3 \end{matrix}]$ , by expanding by minors along the first row.